Context. The LOw Frequency ARray (LOFAR) radio telescope is a giant digital phased array interferometer with multiple antennas
distributed in Europe. It provides discrete sets of Fourier components of the sky brightness. Recovering the original brightness
distribution with aperture synthesis forms an inverse problem that can be solved by various deconvolution and minimization
methods.Aims. Recent papers have established a clear link between the discrete nature of radio interferometry measurement
and the "compressed sensing" (CS) theory, which supports sparse reconstruction methods to form an image from the measured
visibilities. Empowered by proximal theory, CS offers a sound framework for efficient global minimization and sparse data
representation using fast algorithms. Combined with instrumental direction-dependent effects (DDE) in the scope of a real
instrument, we developed and validated a new method based on this framework.Methods. We implemented a sparse reconstruction
method in the standard LOFAR imaging tool and compared the photometric and resolution performance of this new imager with
that of CLEAN-based methods (CLEAN and MS-CLEAN) with simulated and real LOFAR data.Results. We show that i) sparse reconstruction
performs as well as CLEAN in recovering the flux of point sources; ii) performs much better on extended objects (the root
mean square error is reduced by a factor of up to 10); and iii) provides a solution with an effective angular resolution 2−3
times better than the CLEAN images.Conclusions. Sparse recovery gives a correct photometry on high dynamic and wide-field
images and improved realistic structures of extended sources (of simulated and real LOFAR datasets). This sparse reconstruction
method is compatible with modern interferometric imagers that handle DDE corrections (A- and W-projections) required for current
and future instruments such as LOFAR and SKA.

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